I Am the Reinforcements - Respond to an SOS flare, and help complete 10 quests.
For this achievement, the quest length, quest specifics, and number of players do not matter. It's 10 culmulative quests where you get dropped in that matter. Failing does not count, and killing or capturing creatures doesen't matter as long as the quest is completed, the method is irrelevant.
In order to go on a Sortie of this type, go to either your Guildmarm (lady at the canteen) or any of the quest boards around Astera:
Go to: Join a Quest,
Respond to SOS,
You can set preferences (for expediency go to Difficulty and switch it to Low Rank),
Search for SOS Flares,
Pick any of the quests that appear (not expeditions though as they do not count),
And ready up for departure. Complete the quest, and 1/10 is done!